Given: $(i)$. $2, 79, 404$$(ii)$. $30, 06, 194$$(iii)$. $28, 06, 196$$(iv)$. $1, 20, 719$$(v)$. $20, 068$To do: To write the above numbers in the expanded forms.Solution:$(i)$. $2, 79, 404$$=200000+70000+9000+400+00+4\times1$$=2\times10000+7\times10000+9\times10000+4\times100+00+4\times1$$=2\times10^5+7\times10^4+9\times10^3+4\times10^2+0\times10^1+4\times10^0$$(ii)$. $30, 06, 194$$=3000000+0+0+6000+100+90+4$$=3\times1000000+0+0+6\times1000+1\times100+9\times10+4\times1$$=3\times10^6+0\times10^5+0\times10^4+6\times10^3+1\times10^2+9\times10^1+4\times10^0$$(iii)$. $28, 06, 196$$=2000000+800000+0+6000+100+90+6$$=2\times1000000+8\times100000+0+6\times1000+1\times100+9\times10+6\times1$$=2\times10^6+8\times10^5+0\times10+6\times10^3+1\times10^2+9\times10^1+6\times10^0$$(iv)$. $1, 20, 719$$=1000000+20000+0+700+10+9$$1\times100000+2\times10000+0+7\times100+10\times1+9\times1$$=1\times10^5+2\times10^4+0+7\times10^2+1\times10^1+9\times10^0$$(v)$. $20, 068$$=20000+00+00+60+8$$=2\times10000+0\times1000+0\times100+6\times10+8\times1$$=2\times10^4+0\times10^3+0\times10^2+6\times10^1+8\times10^0$Read More

Given:$(a)$. $8\times10^4+6\times10^3+0\times10^2+4\times10^1+5\times10^0$$(b)$. $4\times10^5+5\times10^3+3\times10^2+2\times10^0$$(c)$. $3\times10^4+7\times10^2+5\times10^0$$(d)$. $9\times10^5+2\times10^2+3\times10^1$To do: To find the number from each of the following expanded forms.Solution: $(a)$. $8\times10^4+6\times10^3+0\times10^2+4\times10^1+5\times10^0$ $=8\times10000+6\times1000+0\times100+4\times10+5\times1$$=80000+6000+0+40+5$$=86, 045$$(b)$. $4\times10^5+5\times10^3+3\times10^2+2\times10^0$ $=4\times100000+5\times1000+3\times100+2\times1$$=400000+5000+300+2$$=405302$$(c)$. $3\times10^4+7\times10^2+5\times10^0$$=3\times10000+7\times100+5\times1$$=30000+700+5$$=30705$$(d)$. $9\times10^5+2\times10^2+3\times10^1$ $=9\times100000+2\times100+3\times10$$=900230$Read More

Given: $(i)$. $5,00,00,000$ $(ii)$. $70,00,000$ $(iii)$. $3,18,65,00,000$$(iv)$. $3,90,878$ $(v)$. $39087.8$ $(vi)$ $3908.78$To do: To express the above numbers in standard form.Solution: $(i)$. $5,00,00,000$$=5\times10000000$$=5\times10^7$$(ii)$. $70,00,000$$=7\times1000000$$=7\times10^6$$(iii)$. $3,18,65,00,000$$=3.1865\times 10^9$$(iv)$. $3,90,878$$=3.90878\times10^5$$(v)$. $39087.8$$=390878\times 10^4$$(vi)$ $3908.78$$=3.90878\times 1000$$=3.90878\times 10^3$

Given: Statements: $(a)$ The distance between Earth and Moon is $384, 000, 000\ m$.$(b)$ Speed of light in vacuum is $300, 000, 000\ m/s$.$(c)$ Diameter of the Earth is $1, 27, 56, 000\ m$.$(d)$ Diameter of the Sun is $1, 400, 000, 000\ m$.$(e)$ In a galaxy there are on ... Read More

Given:The length and breadth of a rectangle are \( 10 \mathrm{~cm} \) and \( 20 \mathrm{~cm} \).To do:We have to find the length of its diagonal.Solution:We know that, Length of the diagonal of a rectangle of length $l$ and breadth $b$ is $\sqrt{l^2+b^2}$The length of the rectangle $=10\ cm$The breadth ... Read More

To do:We have to find the square root of the given numbers using the division method.Solution:(i) Square root of 529 is, 232529443129129   0Therefore, The square root of 529 is 23.(ii) Square root of 1369 is, 3731369 967  469  469   0Therefore, The square root of 1369 is 37.(iii) Square root of 363609 ... Read More

Common Factor:A common factor is a whole number which is a factor of two or more numbers. Common Multiples:The multiples which are shared by a given set of numbers are called common multiples.For example:Factors of 10 are 1, 2, 5, 10Factors of 20 are 1, 2, 4, 5, 10, 20Common factors ... Read More

Given: Some figures have more than one line of symmetry as shown in the given figures. Such figures are said to have multiple lines of symmetry.To do: To identify multiple lines of symmetry, if any, in each of the given figures.Solution: In order to check the symmetry and find their lines ... Read More

Given:Given number is $4 . \overline{26}$.To do:We have to visualise the representation of $4 . \overline{26}$ on the number line using successive magnification.Solution:$4 . \overline{26}$ up to 4 decimal places is 4.2626.Therefore, $4.2626$ lies between 4 and 5.So, we divide the number line into 10 equal parts and mark each ... Read More

Given:A number $0.99999\ ....$To do:We have to express $0.99999\ ....$ in the form $\frac{p}{q}$.Solution:Let $x=0.99999.....$_________(i)Multiplying equation (i) by $10$, we get, $10x=9.9999.....$_______(ii)Subtract (i) from (ii), we get, $10x-x=9.9999.......-0.9999.........$$\Rightarrow 9x=9$$\Rightarrow x=\frac{9}{9}=1$Here, $p=1$ and $q=1$Therefore, $0.9999....=1$The difference between 1 and 0.999999 is 0.000001 which is negligible.Hence, we can conclude that 0.999 is ... Read More